I can't access that link. Why not upload the drawing to this Forum to save us having to go somewhere else?
Remember that 12v car batteries can have voltages well above 12 and even above 13. Mine go to 14.7 - 14.9 while being charged.
If you mean that you want the Arduino to control something else that uses 12v then, yes, a transistor or relay can be used to allow the 5v system to control the 12v system. The Arduino probably can't supply enough current to drive a relay directly so you would also need a transistor between the Arduino and the relay coil.
...R